Take up the White Man's burden-- No tawdry rule of kings, But toil of serf and sweeper-- The tale of common things.
After another helping of the same old refrain, our speaker lets us know that these white men are not signing on for glory. Nope, it's not about a "tawdry" (cheap) display of authority. This is work, real work (or "toil," as it's put here).
In fact, the White Man is metaphorically compared to a medieval servant ("serf") or a domestic worker ("sweeper"). This is gritty and unglamorous work, he wants us all to know.
The ports ye shall not enter, The roads ye shall not tread, Go mark them with your living, And mark them with your dead.
And, hey, it gets even worse for our poor White Man. What's the reward for all that unglorified labor? Well, it's certainly not a chance to enjoy all the fruits of that hard work, if that's what you were thinking.
No, the White Man will not be able to stroll through the ports he helps to build or walk along ("tread") the roads he helps to pave. Form-wise, the poem really drives that home here with the use of anaphora in this stanza, repeating "The [blank] ye shall not [blank]" and "mark them with your [blank]." (Check out "Form and Meter" for more on that.)
These aspects of European civilization will be a legacy, one that the White Man doesn't get to enjoy, but rather leaves behind.
At the same time, he will have made his "mark"—both in terms of the designs he brings (while "living") to the "uncivilized" land, as well as the bodies of the hard-working dead white guys who, in some way or another, have met their end by "helping" the locals.